Leverage
BUSI 721
Jones Graduate School of Business
Rice University
Kerry Back
Investing borrowed money is called leverage.
Your own money gains extra force.
The return, good or bad, on each $1 is amplified.
Example
Invest $100,000. Borrow $50,000. Buy $150,000 of stocks.
| Assets | Liabilities |
|---|---|
| Stocks 150,000 | Debt 50,000 |
| Equity |
|---|
| 100,000 |
- Leverage ratio = assets to equity.
- You are levered 1.5 to 1.
A Possible Ending to the Story
Suppose the stocks go up 10% and you’re charged 2% interest on the loan.
| Assets | Liabilities |
|---|---|
| Stocks 165,000 | Debt 51,000 |
| Equity |
|---|
| 114,000 |
- You made 10% plus one half of (10% minus 2%) \(= 0.10 + 0.5(0.10-0.02) = 0.14\)
- “one-half” because you borrowed 50%.
Conclusion
You make the stock return plus the fraction borrowed times (stock return minus borrowing rate).
Another possible ending
- Suppose the stocks fell by 10%.
- You lose 10% plus one half of (\(-\) 10% \(-\) 2% ).
- So, your loss is 16% on your $20,000 investment.
| Assets | Liabilities |
|---|---|
| Stocks 135,000 | Debt 51,000 |
| Equity |
|---|
| 84,000 |
The good and the bad
- You always make the stock return plus the fraction borrowed times (stock return minus borrowing rate).
- With 50% leverage and a 2% interest charge,
\[+10\text{%} \rightarrow +14\text{%}\]
\[-10\text{%} \rightarrow -16\text{%}\]
Margin loan rates
- It pays to shop around.
- Interactive Brokers charges
- the Fed Funds rate plus 1.5% on the first $100,000,
- and falling further after that.
- Oct 1, 2022:
- Fed Funds rate = 3.08%
- Prime rate = 6.25%